id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4465	Guldurdek, Asli	A Short Introduction to Similarity via Ideals	2022	4	.pdf	application/pdf	1873	130	78	In this work, we introduce the notion of similarity between topologies τ1 and τ2, on a set X via ideals. Let X be a set, τ1, τ2 be two given topologies, and I be an ideal on X. We say that τ1 and τ2 are similar with respect to I or I-similar and denote by τ1 ∼I τ2 if, for every nonempty U ∈ τ1, there exists a nonempty V ∈ τ2 such that V \U ∈ I, and for every U ∈ τ2, there exists a nonempty V ∈ τ1 such that V \ U ∈ I. It is clear that if τ1 and τ2 are similar topologies, then they are similar with respect to any ideal I. On the other hand the following example shows that ideal similarity does not imply similarity between topologies.	cache/ejpam-4465.pdf	txt/ejpam-4465.txt